rmevspec: Random samples from spectral distributions of multivariate... In mev: Modelling of Extreme Values

 rmevspec R Documentation

Random samples from spectral distributions of multivariate extreme value models.

Description

Generate from Qi, the spectral measure of a given multivariate extreme value model based on the L1 norm.

Usage

```rmevspec(
n,
d,
param,
sigma,
model = c("log", "neglog", "bilog", "negbilog", "hr", "br", "xstud", "smith",
"schlather", "ct", "sdir", "dirmix", "pairbeta", "pairexp", "wdirbs", "wexpbs"),
weights = NULL,
vario = NULL,
coord = NULL,
grid = FALSE,
dist = NULL,
...
)
```

Arguments

 `n` number of observations `d` dimension of sample `param` parameter vector for the logistic, bilogistic, negative bilogistic and extremal Dirichlet (Coles and Tawn) model. Parameter matrix for the Dirichlet mixture. Degree of freedoms for extremal student model. See Details. `sigma` covariance matrix for Brown-Resnick and extremal Student-t distributions. Symmetric matrix of squared coefficients λ^2 for the Husler-Reiss model, with zero diagonal elements. `model` for multivariate extreme value distributions, users can choose between 1-parameter logistic and negative logistic, asymmetric logistic and negative logistic, bilogistic, Husler-Reiss, extremal Dirichlet model (Coles and Tawn) or the Dirichlet mixture. Spatial models include the Brown-Resnick, Smith, Schlather and extremal Student max-stable processes. `weights` vector of length `m` for the `m` mixture components. Must sum to one `vario` semivariogram function whose first argument must be distance. Used only if provided in conjunction with `coord` and if `sigma` is missing `coord` `d` by `k` matrix of coordinates, used as input in the variogram `vario` or as parameter for the Smith model. If `grid` is `TRUE`, unique entries should be supplied. `grid` Logical. `TRUE` if the coordinates are two-dimensional grid points (spatial models). `dist` symmetric matrix of pairwise distances. Default to `NULL`. `...` additional arguments for the `vario` function

Details

The vector param differs depending on the model

• `log`: one dimensional parameter greater than 1

• `neglog`: one dimensional positive parameter

• `bilog`: `d`-dimensional vector of parameters in [0,1]

• `negbilog`: `d`-dimensional vector of negative parameters

• `ct`, `dir`, `negdir`: `d`-dimensional vector of positive (a)symmetry parameters. Alternatively, a d+1 vector consisting of the `d` Dirichlet parameters and the last entry is an index of regular variation in (0, 1] treated as scale

• `xstud`: one dimensional parameter corresponding to degrees of freedom `alpha`

• `dirmix`: `d` by `m`-dimensional matrix of positive (a)symmetry parameters

• `pairbeta, pairexp`: `d(d-1)/2+1` vector of parameters, containing the concentration parameter and the coefficients of the pairwise beta, in lexicographical order e.g., β_{1,2}, β_{1,3}, …

• `wdirbs, wexpbs`: `2d` vector of `d` concentration parameters followed by the `d` Dirichlet parameters

Value

an `n` by `d` exact sample from the corresponding multivariate extreme value model

Note

This functionality can be useful to generate for example Pareto processes with marginal exceedances.

Leo Belzile

References

Dombry, Engelke and Oesting (2016). Exact simulation of max-stable processes, Biometrika, 103(2), 303–317.

Boldi (2009). A note on the representation of parametric models for multivariate extremes. Extremes 12, 211–218.

Examples

```set.seed(1)
rmevspec(n=100, d=3, param=2.5, model='log')
rmevspec(n=100, d=3, param=2.5, model='neglog')
rmevspec(n=100, d=4, param=c(0.2,0.1,0.9,0.5), model='bilog')
rmevspec(n=100, d=2, param=c(0.8,1.2), model='ct') #Dirichlet model
rmevspec(n=100, d=2, param=c(0.8,1.2,0.5), model='sdir') #with additional scale parameter
#Variogram gamma(h) = scale*||h||^alpha
#NEW: Variogram must take distance as argument
vario <- function(x, scale=0.5, alpha=0.8){ scale*x^alpha }
#grid specification
grid.coord <- as.matrix(expand.grid(runif(4), runif(4)))
rmevspec(n=100, vario=vario,coord=grid.coord, model='br')
## Example with Dirichlet mixture
alpha.mat <- cbind(c(2,1,1),c(1,2,1),c(1,1,2))
rmevspec(n=100, param=alpha.mat, weights=rep(1/3,3), model='dirmix')
```

mev documentation built on April 26, 2022, 1:07 a.m.